Connecting the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments

Abstract

The one-band and three-band Hubbard models which describe the electronic structure of cuprates indicate very different values of effective electronic parameters, such as the on-site Coulomb energy and the hybridization strength. In contrast, a comparison of electronic parameters of several cuprates with corresponding values from spectroscopy and scattering experiments indicates similar values in the three-band model and cluster model calculations used to simulate experimental results. The Heisenberg exchange coupling $J$ obtained by a downfolding method in terms of the three band parameters is used to carry out an optimization analysis consistent with $J$ from neutron scattering experiments for a series of cuprates. In addition, the effective one-band parameters $\tilde{U}$ and $\tilde{t}$ are described using the three band parameters, thus revealing the hidden equivalence of the one-band and three-band models. The ground-state singlet weights obtained from an exact diagonalization elucidates the role of Zhang-Rice singlets in the equivalence. The results provide a consistent method to connect electronic parameters obtained from spectroscopy and the three-band model with values of $J$ obtained from scattering experiments, band dispersion measurements and the effective one-band Hubbard model.

arXiv comment9 pages, 1 figure (submitted to Physical Review B)

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• Effective one-band models for the 1D cuprate Ba${}_{2-x}$Sr${}_x$CuO${}_{3+\delta }$
• Cavity-Enhanced Optical Manipulation of Antiferromagnetic Magnon-Pairs
• Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds
• First principle prediction of structural distortions in the cuprates and their impact on the electronic structure
• Oxygen on-site Coulomb energy in Pr${}_{1.3-x}$La${}_{0.7}$Ce${}_x$CuO${}_4$ and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ and its relation with Heisenberg exchange
• Influence of oxygen orbitals and boundary conditions on the pairing behavior in the Emery model for doped ladders
• Update of Hartree--Fock theory for Hubbard-like models